A multiple choice test has 10 questions, each of which has 4 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer exactly 3 questions correctly? Round your answer to four decimal places.
Accepted Solution
A:
Answer:0.2503Step-by-step explanation:To solve this , we use the Bernoulli trial equation. Now, there are 10 questions with 4 options each. The total number of options is thus = 10 × 4 = 40 optionsThere are only 10 correct answers however. The probability of picking a correct answer is thus 1/4 or 0.25Now we know there are 30 wrong options. The probability of picking a wrong option is 30/40 or 0.75To answer 3 questions correctly, it means she would answer 7 wrongfully. Now to complete the parameters for the bernoulli trial, we know she is making 3 correct choices. Now the number of ways to select three correct choices out of 10 is 10C3Computing the Bernoulli trial, we have :(10C3) × (0.25)^3 × (0.75)^10= 0.2503